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Let X= _ x=0 ^n ( (-1)^r r+1 ) , then |X- 2| will be

Options

  1. Agreater than 1 2(n+1)
  2. Bgreater than 1 2(n+2)
  3. Cless than 1 2(n+1)
  4. Dless than 1 2(n+2)

Correct answer

C. less than 1 2(n+1)

Step-by-step solution

1-x+x^2-x^3+ +(-x)^n= 1+(-1)^n x^ n+1 1+x ₀^1 (1-x+x^2-x^3+ +(-x)^n ) d x= ₀^1 ( 1 1+x ) d x+(-1)^n ₀^1 ( x^ n+1 1+x ) d x |X- 2|= ₀^1 ( x^ n+1 1+x ) d x , where 1 2(n+2) ₀^1 ( x^ n+1 1+x ) d x 1 2(n+1)

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